# Particles in an Electromagnetic Field

• Alberto Galindo
• Pedro Pascual
Part of the Texts and Monographs in Physics book series (TMP)

## Abstract

It is well known [JA 75] that in classical electrodynamics, an electromagnetic field is described by the electric and magnetic fields E(r; t),B(r; t). These fields satisfy Maxwell’s equations, which in unrationalized Gaussian units become
$$\begin{gathered}\nabla \times E\left( {r;t} \right) + \frac{1}{c}\frac{{\partial B\left( {r;t} \right)}}{{\partial t}} = 0, \hfill \\\nabla \cdot E\left( {r;t} \right) = 4\pi {\ell _e}\left( {r;t} \right), \hfill \\\nabla \times B\left( {r;t} \right) - \frac{1}{c}\frac{{\partial E\left( {r;t} \right)}}{{\partial t}} = \frac{{4\pi }}{c}{J_{em}}\left( {r;t} \right), \hfill \\\end{gathered}$$
(12.1)
where ϱe(r; t) and J em (r; t) are respectively the charge and current densities, related by the continuity equation
$$\frac{{{\partial _{{\varrho _e}}}\left( {r;t} \right)}}{{\partial t}} + \nabla \cdot{J_{em}}\left( {r;t} \right) = 0$$
(12.2)
.

## Keywords

Magnetic Field Electromagnetic Field Orbital Angular Momentum SchrOdinger Equation Pauli Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.